Understanding SAE J1987: The Force and Moment Test Method for Passenger and Light Truck Tires

The SAE J1987 recommended practice has long served as a reference for accurately determining the steady-state force and moment properties of passenger car and light truck tires. This standardized test method, performed on a belt-type flat surface machine, enables engineers to evaluate five key tire forces and moments as functions of slip angle and normal force. Although the document was stabilized in 2020 and is no longer actively maintained, its definitions, procedures, and normalization techniques continue to inform research, development, quality control, and vehicle dynamics modeling. This article summarizes the essential aspects of the standard, offers practical engineering insights, and answers common questions about its application. 🛠️

1. Scope and Purpose of the Standard

The test method described in SAE J1987 applies exclusively to passenger car and light truck tires. It is performed on a laboratory test machine that simulates a flat roadway with a continuous belt surface. The method is designed to measure five tire forces and moments—lateral force, longitudinal force, normal force, overturning moment, rolling moment, and aligning moment—under steady-state, free-rolling conditions. The test involves incrementally changing slip angle and normal force in a prescribed sequence, allowing the characterization of key tire behavior such as cornering stiffness and aligning stiffness.

Heavy-duty tires are explicitly excluded from this standard because the force and moment ranges required for those tires would compromise the sensitivity needed for passenger and light truck tire measurements. The standard is intended for comparative evaluations, making it suitable for R&D, manufacturing quality control, and vehicle dynamics model validation. Correlation between different test machines can be verified using the procedures outlined in the document.

2. Key Definitions and Test Parameters

The standard establishes precise definitions for fundamental tire properties and test conditions. The table below summarizes the most important terms engineers should know when working with this method.

The tire axis system, defined in the standard, uses a right-hand orthogonal coordinate system with the origin at the center of tire contact. The X’ axis points forward, Y’ to the right (in the direction of travel), and Z’ downward into the road plane. Forces and moments are defined accordingly, with explicit positive directions. Aligning moment and lateral force offsets, which depend on tire rotation direction (left or right), are also addressed.

The standard emphasizes the normalization of force and moment properties with respect to normal force. This design insight enables engineers to compare results across different tire sizes, inflation pressures, and service conditions, making the method highly useful for vehicle dynamics parameterization. 🔍

3. Test Apparatus and Procedure

The laboratory test machine consists of three main components: a belt-type flat surface simulated roadway with a drive mechanism, a loading and positioning system, and a measuring system. The roadway surface is coated with a stable, nonpolishing material such as Safety Walk™ or 3-Mite™ and must be kept free of loose material or deposits. The supporting structure must be sufficiently rigid to maintain angular accuracy, and the bearing system must have less than 0.5 mm of wear and be maintained at 24 °C ± 2.5 °C. The surface friction and flatness must be periodically checked, with any visible defects (cracks, tears, dimples, contaminants) prompting surface replacement.

The test procedure involves incrementally changing slip angle and normal force in a defined sequence while the tire is free-rolling under steady-state conditions. The standard does not prescribe a specific order but requires consistent implementation to ensure repeatability. The five measured outputs include lateral force, longitudinal force, normal force, overturning moment, rolling moment, and aligning moment. From these, cornering stiffness and aligning stiffness can be calculated.

Engineering Design Insight: A key strength of SAE J1987 is its normalization of force and moment properties with respect to normal force. This allows engineers to build tire models that are scalable across load conditions, a critical factor in vehicle dynamics simulation. The use of a belt-type flat surface also eliminates curvature effects seen in drum testers, providing closer approximation to real-world flat road conditions—though correlation with actual vehicle behavior still requires careful validation.

Frequently Asked Questions

How are the five tire forces and moments measured under steady-state free-rolling conditions?

The forces and moments are measured using a load cell or transducer system integrated into the spindle or test fixture. The tire is loaded against the moving belt at a controlled normal force and slip angle, and the resulting reactions are recorded after steady-state conditions are achieved (i.e., when readings stabilize). The system simultaneously captures lateral force, longitudinal force, normal force, overturning moment, rolling moment, and aligning moment as defined by the tire axis system.

What is the recommended sequence for changing slip angle and normal force during testing?

SAE J1987 specifies that slip angle and normal force should be changed incrementally, but it does not mandate a single sequence. Typically, a matrix of slip angles (e.g., from –10° to +10° in 1° or 2° steps) is run at several normal force levels (from 20% to 160% of target load). The exact order should be designed to minimize hysteresis and thermal effects; many practitioners use a progression from low to high slip angle or a randomized block design. The key is to maintain free-rolling conditions (no applied torque) and to allow sufficient stabilization time at each test point.

How are aligning stiffness and cornering stiffness calculated from the test data?

Cornering stiffness is the slope of the lateral force vs. slip angle curve at zero slip angle. Practically, it is often approximated as the absolute difference in lateral force between –1° and +1° slip angle divided by 2. Similarly, aligning stiffness is the slope of the aligning moment vs. slip angle curve at zero slip angle, approximated by subtracting the aligning moment at –1° from that at +1° and dividing by 2. The standard defines coefficients as these stiffness values divided by the absolute normal force, enabling normalization across different loads.

Why are heavy-duty tires excluded from this standard?

Heavy-duty tires (e.g., for trucks and buses) generate significantly larger forces and moments, which would require measurement systems with much higher force ranges. Such systems would lack the sensitivity needed to accurately capture the relatively smaller forces and moments from passenger car and light truck tires. Although a dedicated standard for heavy-duty tires would share many of the same measurement concepts, the hardware would need substantial modifications to accommodate the different load levels. As a result, SAE J1987 is explicitly scoped for passenger and light truck applications only.

In summary, SAE J1987 provides a robust framework for understanding and measuring tire force and moment behavior under controlled laboratory conditions. While the standard is no longer actively updated, its contributions to the tire industry and vehicle dynamics community remain substantial. Engineers working with tire testing or vehicle modeling will benefit from familiarity with its terminology, test setup, and normalization principles. 🛠️